In an Infowars broadcast, Mr Jones announced he would no longer “pigheadedly” support Mr Trump.
Mr Jones, who has been a supporter of the former president, said he disagreed with Mr Trump over Covid vaccines but supported him anyway.
The former president, now at the centre of a search conducted by the Federal Bureau of Investigation (FBI) last week at Mar-a-Lago in connection with “classified nuclear documents”, still wields considerable influence in the Republican party.
Mr Jones said he had disagreed with Operation Warp Speed – the initiative launched by the Trump administration in May 2020 to fast track the development and production of Covid vaccines that aimed to help inoculate 300m people by January 2021.
The right-wing conspiracy theorist said Mr Trump needed his support at the time to prevent the “nightmare scenario” of Joe Biden being elected president.
“That said, I am supporting DeSantis. DeSantis has just gone from being awesome to being unbelievably good,” said Mr Jones.
“I can look into his eyes on HD video, and I see the real sincerity.”
“We have someone who is better than Trump. Way better than Trump,” Mr Jones said, adding that the Florida governor is the person Mr Trump “should be like”.
Alex Jones on Desantis: “We have someone who is better than Trump. Way better than Trump.” pic.twitter.com/npwQY6NwOu
— Ron Filipkowski 🇺🇦 (@RonFilipkowski) August 18, 2022
Both the Florida governor and the former president are favourites for the Republican ticket for the 2024 presidential elections, though neither have made any official announcement yet.
This is not the first time Mr Jones has lashed out at Mr Trump for his vaccine policy.
In December, he warned the former president by calling him either “ignorant” or “evil” for encouraging people to take the vaccine.
He is also being probed by the FBI and the Department of Justice for his role in last year’s Capitol riot.
According to a report earlier this month, the Jan 6 committee is preparing to subpoena Mr Jones’ texts and emails that were accidentally sent to an attorney for the Sandy Hook victims.
The far-right conspiracy theorist lost a defamation suit launched by the families of victims of the Sandy Hook shooting for false claims that the massacre, in which 26 people were shot and killed at the elementary school in Newtown in 2012, wasn’t real.
He has been ordered to pay $45.2m in punitive damages to the family of a victim in addition to $4.11m in compensatory damages.